Note on Min- k-Planar Drawings of Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139105" target="_blank" >RIV/00216224:14330/24:00139105 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPICS.GD.2024.8" target="_blank" >http://dx.doi.org/10.4230/LIPICS.GD.2024.8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPICS.GD.2024.8" target="_blank" >10.4230/LIPICS.GD.2024.8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Note on Min- k-Planar Drawings of Graphs

Popis výsledku v původním jazyce

The k-planar graphs, which are (usually with small values of k such as 1,2,3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently introduced [Binucci et al., GD 2023] min-k-planar drawings of graphs, edges may possibly carry more than k crossings, but in any two crossing edges, at least one of the two must have at most k crossings. In both concepts, one may consider general drawings or a popular restricted concept of drawings called simple. In a simple drawing, every two edges are allowed to cross at most once, and any two edges which share a vertex are forbidden to cross. While, regarding the former concept, it is for k ≤ 3 known (but perhaps not widely known) that every general k-planar graph admits a simple k-planar drawing and this ceases to be true for any k ≤ 4, the difference between general and simple drawings in the latter concept is more striking. We prove that there exist graphs with a min-2-planar drawing, or with a min-3-planar drawing avoiding crossings of adjacent edges, which have no simple min-k-planar drawings for arbitrarily large fixed k.

Název v anglickém jazyce

Note on Min- k-Planar Drawings of Graphs

Popis výsledku anglicky

The k-planar graphs, which are (usually with small values of k such as 1,2,3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently introduced [Binucci et al., GD 2023] min-k-planar drawings of graphs, edges may possibly carry more than k crossings, but in any two crossing edges, at least one of the two must have at most k crossings. In both concepts, one may consider general drawings or a popular restricted concept of drawings called simple. In a simple drawing, every two edges are allowed to cross at most once, and any two edges which share a vertex are forbidden to cross. While, regarding the former concept, it is for k ≤ 3 known (but perhaps not widely known) that every general k-planar graph admits a simple k-planar drawing and this ceases to be true for any k ≤ 4, the difference between general and simple drawings in the latter concept is more striking. We prove that there exist graphs with a min-2-planar drawing, or with a min-3-planar drawing avoiding crossings of adjacent edges, which have no simple min-k-planar drawings for arbitrarily large fixed k.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

ISBN

9783959773430

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

10

Strana od-do

„8:1“-„8:10“

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Wien, Austria

Datum konání akce

1. 1. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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